Lead Concentration vs. Setback Distance Given Day-of-the-Week,
Week, and Height

Below is a trellis display of lead concentration against setback distance
given day-of-the-week (thu-wed), week (1-3), and height (3 values).
There are 63 panels arranged into 31 columns and 3 rows. Each row
conditions on a different value of height; as we go from bottom to top,
the heights increase. The panels in each row are in time order because
the panels first cycle through the days of the week and then through the
weeks.

The display reveals much about the structure of the data.
There is a strong interaction between height and setback distance.
For the lowest height, lead
decreases with setback. But for the middle value of height, lead typically
first increases with setback and then decreases. For the highest height,
lead occasionally has the increase-decrease pattern for about 1/3 of
the days, most of them days with large concentrations, and is
relatively stable for the remaining days. This behavior is consistent
with air transport mechanisms. Lead is emitted at ground level from
automobile tail pipes. The closest of the 9 monitors, the one with
the lowest height and the closest setback, has the largest
concentrations because
it is close to the pollution source.
From the source, the lead is carried laterally by the wind,
spreading upward as it moves. This plume-like behavior can cause
the concentrations to be relatively small at the higher monitors
at the closest setback.

Barley Yield vs. Variety and Year Given Site

The following figure is a Trellis display
of data from an agricultural field trial
to study the crop barley.
At six sites in Minnesota, ten varieties of barley
were grown in each of two years.
The data are the yields for all combinations of site,
variety, and year, so there are 6 X 10 X 2 = 120 observations.
Each panel in the figure displays the 20 yields
at a single site.

The barley experiment was run in the 1930s.
The data first appeared in a 1934 report published
by the experimenters.
Since then, the data have been analyzed and re-analyzed.
R. A. Fisher presented the data for five of the sites in his classic book,
The Design of Experiments.
Publication in the book made the data famous, and many others
subsequently analyzed the them, usually to illustrate
a new statistical method.

Then in the early 1990s, the data were visualized by Trellis Graphics.
The result was a big surprise. Through 60 years and many
analyses, an important happening in the data had gone undetected.
The above figure shows the happening, which occurs
at Morris. For all other sites, 1931 produced a significantly higher
overall yield than 1932.
The reverse is true at Morris. But most importantly, the amount by which
1932 exceeds 1931 at Morris is similar to the amounts
by which 1931 exceeds 1932 at the other sites.
Either an extraordinary natural event, such as disease or a local
weather anomaly, produced a strange coincidence, or the years for
Morris were inadvertently reversed.
More Trellis displays, a statistical modeling of the data, and some
background checks on the experiment led
to the conclusion that the data are in error.
But it was Trellis displays such as the above figure that
provided the ``Aha!'' which led to the conclusion.

Sunspot Numbers vs. Time

The top panel graphs the yearly
sunspot numbers from 1849 to 1924. The aspect ratio,
the height of the data region of the graph divided by
the width, is 1.0. An aspect ratio of 1.0 is what you might
expect to see as a default in cases where aspect ratio has not
been considered. But the graph fails to reveal an important
property of the cycles.
In the bottom panel, the data are graphed
again, but this time the aspect ratio has been chosen by a trellis
algorithm called
banking to 45 degrees.
Now the property is revealed.
The sunspot cycles typically rise more rapidly than they fall;
this behavior is pronounced for the cycles with high
peaks, is less pronounced for those with medium peaks,
and disappears for those cycles with the lowest peaks.
In the top panel, the aspect ratio of 1.0 prevents an
accurate visual decoding of the slopes of the line segments
connecting successive observations.
In the bottom panel, banking allows a more accurate
visual decoding of the slopes.